Real identity in the world is defined in terms of coincidence of properties: objects are identical if they both determinately have and determinately lack the same properties, and they are distinct if one determinately has a property that the other determinately lacks.

If neither of these holds, then it is indeterminate whether the objects are identical.

It is an empirical matter whether there is any indeterminacy at all, and an empirical matter whether such indeterminacy, if it exists, extends to identity.

This explanation of identity validates Leibniz's Law2: From 'a = b' and 'φa' one can infer 'φb'.

But it does not validate the contrapositive form of this law: one might have 'φa' and '¬φb' both true without '¬a = b' being true; this can happen if 'φx' does not express a property.

The four identity puzzles are reviewed; in each case in which the identity is indeterminate, there is a property determinately possessed by one object that is not determinately possessed by the other, but there is no property for which they determinately disagree.